Here, \(f_T(z; T, q, p)\)  is a function of altitude \(z\)  and of the thermodynamic state of an atmospheric column (dependent on temperature \(T\) , pressure \(p\) , and specific humidity \(q\)  in the column), which determines where and when the convection scheme is active; \(f_q(T, q, p)\)  is a function that modulates the relaxation of the specific humidity in non-precipitating (shallow) convection [1]}, [2]}. The reference temperature profile is a moist adiabat, \(T_\mathrm {ma}(z)\) , shifted by a state-dependent and constant-with-height offset \(\Delta T\) , which is chosen to ensure conservation of enthalpy integrated over a column: \(T_\mathrm {ref}(z) = T_\mathrm {ma}(z) + \Delta T\) . The reference specific humidity \(q_\mathrm {ref}(z)\)  is the specific humidity corresponding to a fixed relative humidity RH relative to the moist adiabat \(T_\mathrm {ma}(z)\) . The two key parameters in this simple convection scheme thus are the timescale \(\tau \)  and the relative humidity parameter RH. We demonstrate how we can learn about them from synthetic data generated with the GCM.
